How do I update iOS on my iPhone 6s Plus?

You can update an iPhone 6s Plus to the latest release of iOS 15. You cannot update it to iOS 16 or later.

About iOS 15 Updates - Apple Support

Update your iPhone or iPad - Apple Support

Updating iOS: common issues and solutions - Apple Community

The 's' in the model name is significant. For an iPhone 6 Plus (no "s"), iOS 12 is the end of the line.

An iPhone 6s, iPhone 6s Plus, iPhone 7, iPhone 7 Plus, or iPhone SE 1 isn't capable of 16 or above; they require an A11 or better CPU. To install 15.8.3, use a computer or the Software Update function in Settings.

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You can upgrade your iPhone 6s Plus by going to Settings > General > Software Update. If an update is available, it will show up there, and you can download and install it directly. Make sure your phone is charged and connected to Wi-Fi before starting the update.